Charo is 50 feet from the tallest totem pole, located in Alberta Bay, Canada, which has a height of 173 feet. If Charo’s eyes are 5 feet from the ground, find the angle to the nearest degree of elevation for her line of sight to the top of the totem.
To find the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the line of sight and the horizontal ground.
Let's denote the height of the totem pole as "h" and the distance from Charo to the totem pole as "d".
Given:
Height of the totem pole (h) = 173 feet
Distance from Charo to the totem pole (d) = 50 feet
Charo's eye level from the ground = 5 feet
First, we need to calculate the total height of the totem pole from Charo's eye level:
Total height = height of totem pole + Charo's eye level
Total height = 173 feet + 5 feet
Total height = 178 feet
Now, we can use trigonometry to find the angle of elevation:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = total height/distance from Charo to totem pole
tan(angle of elevation) = 178 feet/50 feet
Now we can find the angle of elevation by taking the inverse tangent (arctan) of both sides:
angle of elevation = arctan(178/50)
angle of elevation ≈ 73.74 degrees (rounded to the nearest degree)
Therefore, the nearest degree of elevation for Charo's line of sight to the top of the totem pole is approximately 73 degrees.
To find the angle of elevation, we need to use trigonometry. In this case, we can use the tangent function.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this scenario, the opposite side is the height of the totem pole (173 ft), and the adjacent side is the horizontal distance between Charo and the totem pole (50 ft).
So, we can calculate the tangent of the angle of elevation as:
tan(θ) = opposite / adjacent
tan(θ) = 173 ft / 50 ft
Now, to find the angle itself, we need to take the inverse tangent (arctan) of both sides:
θ = arctan(tan(θ))
θ = arctan(173 ft / 50 ft)
Using a scientific calculator or an online trigonometry tool, we can evaluate the arctan of this ratio to find the angle in radians. Then, we can convert it into degrees.
θ ≈ 73.34 degrees
Therefore, the angle of elevation to the nearest degree is approximately 73 degrees.
The angle is θ, where
tanθ = (173-5)/50